Rubberized Cord Thickness
Measurement Based on Laser
Triangulation – Part I: Technology
Petar B. Petrović
Associate Professor
Faculty of Mechanical Engineering
University of Belgrade
Steel and textile cord coating is one of the key rubber processing
technologies in tiremaking industry. Specifications are very demanding. In
particular, thickness variation across the sheet profile and downstream is
very difficult to fulfill. For in-process thickness measurement the most
common are systems based on non-contact beta or gamma radiation
sensors. Regardless of their wide use, non-contact radiation sensors
possess serious drawbacks: they are measuring thickness in indirect way
only, they are highly sensitive to variations of material properties, and
probably the most critical one, they are potentially dangerous for both
personnel and environment. Recent advances in optoelectronics have
founded new alternative method for non-contact thickness measurement
based on laser triangulation. Extremely delicate optical properties of fresh
calendered rubber and severe environmental conditions create serious
problems in implementation of this technology. This two-part paper
presents a general conceptual framework for in-process laser-based
thickness measurement, and proposes a new method for processing
acquired sensory data based on statistical surface characterization.
Proposed method is experimentally verified, and based on these results the
new measuring systems are developed and implemented in industry.
Keywords: Tire manufacturing, Laser triangulation, Thickness
measusrement.
1. INTRODUCTION
Steel and textile cord coating, i.e., cord rubberizing, is
one of the key rubber processing technologies in
tiremaking industry. Specifications and tolerances of
rubberized cord sheets (RCS) are very demanding. In
particular, thickness variation in lateral direction (across
the sheet profile) and downstream, or machine direction,
as well as the cord density are very difficult to fulfill.
For in-process thickness measurement the most
common are systems based on non-contact beta or
gamma radiation sensors. Regardless of their wide use,
non-contact radioactive sensors possess serious
drawbacks: they measure thickness on indirect way
only, they are highly sensitive to variations of material
properties, and they are potentially dangerous.
Probably, the most serious problem with radiation
sensors is their inherent risk for both, personnel and
environment, which consequently requires costly
maintenance and produces other implications.
Environmental and, more generally, societal risk that
the use of radiation sensors brings to, becomes higher
and higher as related regulative (concerning health,
safety and working conditions) cut down permissible
levels of radiation. Extensive measures carried out by
companies to comply these regulatives seriously rise up
Received: June 2007, Accepted: September 2007.
Correspondence to: Dr Petrović B. Petar, Associate Professor
Faculty of Mechanical Engineering,
Kraljice Marije 16, 11120 Belgrade 35, Serbia
E-mail: [email protected]
© Faculty of Mechanical Engineering, Belgrade. All rights reserved
the costs, which stresses the needs for developing
alternative technology - more environment and human
friendly, but also, having improved measuring
properties, such as better accuracy, robustness and even
surface texture scanning capabilities (high space
resolution), which becomes necessary in order to
enhance quality of the calendering process as well as the
entire quality of products having as ingredient the
rubberized cord.
Optoelectronics and optical sensors that are
dedicated for in-process dimensional metrology had
rapid growth in past decade [1]. They were quickly
introduced in industry with success. Since they offer a
challenging alternative to non-contact radiation sensors,
recently there were attempts of their introduction in
tiremaking industry too. Unfortunately, application of
optical sensors in rubber measurement is generally not
so straightforward.
Laser triangulation sensors measure thickness
directly and they collect data at much higher rates than
radiation sensors can, with no needs for extensive and
frequent recalibration. They have no inherent risk for
personnel or environment too. However, specific
geometrical and optical properties of rubberized cord
surface generate extremely unfavorable measuring
conditions (fresh calendered rubber has a highly
texturized surface, composed of interlaced black and
shiny areas, and usually evaporates smoke or fumes). As
a result, measured data dropout and uncertainty can
become unacceptably high. Therefore, standard optical
sensors cannot be applied effectively using simple
analogy with in-process thickness measurements carried
out in other industry segments (metalworking, pulp and
FME Transactions (2007) 35, 77-84
77
paper, plastic processing, etc). To overcome this
problem it is necessary to use more enhanced optical
sensing systems and extensive processing of measured
data.
This paper presents a general conceptual framework
for in-process thickness measurement of the rubberized
cord using laser triangulation sensors, and proposes a
new method for processing acquired sensory data based
on statistical surface characterization. This paper also
presents two examples of successful application of
developed technology for in-process thickness
measurement and texture profile scanning for both
rubberized steel and textile cord. These measuring
systems are implemented in industrial environment
within the more general projects of modernization of
calendering lines.
where a is the object distance and f E is the focal length
of the lens. When the RCS surface is displaced to a
distance z in the direction collinear with incident laser
beam, the corresponding object distance a' is then:
a ′ = a 2 + 2az cos α + z 2 ,
(2)
where α denotes the angle between incident laser beam
and imaging lens axis (viewing angle). The new image
distance b' is defined by substituting (2) in (1). Image
displacement angle β can be defined using equation (2):
cos β =
a 2 + a′ 2 − z 2
,
2aa′
(3)
or equivalently, concerning image displacement w:
cos β =
2. TECHNOLOGY
b 2 + b′ 2 − w 2
.
2bb ′
(4)
Laser proximity sensor for thickness measurement
applications is based on optical triangulation that serves
as a basic concept for displacement measurement of
diffuse target surface. Basic definitions are given in
standard DIN 32877, 1999 - Optoelectronic
Measurement of Distance, Profile and Form.
Unknown relation between surface displacement z and
image displacement w along the F'F'' line, may be
derived by superimposing equations (3) and (4):
2.1 Optical triangulation
The detector inclination angle is defined by
differentiating image distance vector b’ for arbitrary
displacement z of RCS diffusive surface. From equation
(1) follows:
The optical triangulation system consists of a light
source (usually visible low power semiconductor laser),
condensing lens, converging imaging lens/objective and
position sensitive photo detector (shown in Fig.1). A
light source projects through condensing lens a spot of
light on RCS surface. Since the surface of RCS is not a
perfect mirror, the light will be subjected to diffusion by
reflection, and thus, the light will be scattered in all
directions in a hemisphere around the point D. A portion
of reflected light, passing through imaging lens E, will
be more or less well focused at point F. If the RCS
surface in motion has a component of displacement
collinear to the incident light beam, the displaced light
spot D' will have displacement components in both
parallel and perpendicular direction in respect to the
axis of the imaging lens E. Since the imaging lens
remains stationary, the component of displacement
perpendicular to the imaging lens axis causes a
corresponding displacement of the image F'. In the same
way, another image F'' that corresponds to the new spot
location D'' may be created. The displacement of the
image point F is proportional to the displacement of the
diffusive RCS surface, collinear to the incident light
beam. In order to measure the image displacement, a
position sensing photo detector must be placed along the
line F'F''.
Many triangulation systems are designed with the
detector perpendicular to the main axis of the imaging
lens [2]. In order to keep the image in focus, the
detector must be inclined at an angle γ as it is governed
by the F'F'' line. Applying lens formula, the image
distance b may be defined as:
b=
78 ▪ VOL. 35, No 2, 2007
a fE
,
a − fE
(1)
w=
(a 2 + a′2 − z 2 )bb′ 2
− b + b′2 .
aa′
tan γ =
db′ d a ′ f E
).
= (
dz dz a ′ − f E
(5)
(6)
It is clear from (6) and (2) that detector inclination angle
is nonlinear function of RCS surface displacement.
Figure 1. General outline of optical triangulation concept.
2.2 Photo detector
The triangulation sensors use one of two types of photo
detectors to locate the center of the imaged spot:
position-sensing detector (PSD) which is essentially
analogue device, and one-dimensional photodiode array
which is true digital device (one-dimensional CCD or
CMOS imagers).
FME Transactions
The PSD, also known as a lateral effect photodiode,
is a single-element analog detector that converts
incident light into continuous position data. It has three
terminals, one on the back surface and two on the active
front surface (shown in Fig. 2a). The active surface
behaves as a very homogenous resistance, so that the
current in each contact depends linearly on the light spot
position, or more precisely, on the position of the light
spot center of gravity. The relationship between these
two output currents gives immediately the light spot
position through the relation:
L y − y2
(7)
),
x= ( 1
2 y1 + y 2
where L is the length of the PSD active surface. It is
important that the intensity of the incident light spot
does not affect the calculation of the light spot position.
However, relation (7) also shows that information of the
light spot intensity profile is completely lost. The lost
information content makes PSD sensitive to errors
generated by distortion of Gaussian profile of the
imaged light spot (Fig. 2b).
complementary-metal-oxide-semiconductor
(CMOS)
imager. Besides the differences in underlying
technology, the main difference between them is the
way how they process and transfer data for each pixel.
CCD process pixel data sequentially while CMOS
imager process pixel data in parallel. It means that when
exposure of particular pixel in CCD imager is complete,
each pixel’s charge packet is transfered sequentially to a
common output structure and then processed and sent
off-chip. In a CMOS imager, the charge-to-voltage
conversion takes place in each pixel, i.e., immediately
after shut-off signal processing is performed locally in
parallel way. This difference in readout techniques has
significant implications to sensor architecture,
capabilities, limitations and overall performances.
Although PSD can handle data rates far greater than
the photodiode arrays, and process these data on much
simpler way (is especially a very important simple
mechanism for very fast compensation of overall lightlevel changes), they are not so efficient in RCS
thickness measurement. The ability of digital detectors
to preserve and process the imaged spot profile using
arbitrary complex algorithms, make this technology
preferable in RCS thickness measurement task. Recent
advances in CMOS technology, in particular
improvements in signal to noise performances as well as
the more synchronized shut-off function, enables digital
detectors to run at high sampling frequencies too.
2.3 Surface reflectivity
Figure 2. Operating principle of analogue (a, b) and digital
(c, d) photo detector and their sensitivity to errors.
The one-dimensional array has a light-sensitive
elements or photodiodes arranged in a line as shown in
Fig. 2c. When these photodiodes are exposed to
incoming light, the light is transformed into electrical
charges whose size is proportional to the light intensity.
At the time of registration, collected charges are
transformed into a set of voltages that are directly
proportional to the size of the charges, and thereby
proportional to the intensity of light striking each pixel
of the detector. Besides the space discretization (this
type of detector is in fact an ordered set of pixels), the
voltage output of each pixel is discretized in time and
intensity. Therefore, this type of detector is essentially a
digital device able to preserve complete information
content of the imaged light spot, i.e., its space location,
as well as its intensity profile (shown in Fig. 2d).
In general, digital photodetector can be realized
either as charge coupled device (CCD) imager or as
FME Transactions
Because triangulation operates by imaging the light
reflected from the surface, a change in surface
reflectivity will change the level or intensity of light
reaching the detector. Reflectivity is influenced by
several factors, including the color and surface
waviness/roughness/texture of the object being
measured, [3] and [4].
When a light beam hits the diffusive CR surface, a
certain amount is transmitted through the medium, a
certain amount is absorbed by the medium itself and the
rest of light is reflected. If the reflection coefficient is
designated by Lρ, the transmission coefficient by Lτ and
the absorption coefficient by Lα, it is evident that the
following must be satisfied:
Lρ + L τ + L α = 1 .
(8)
Reflected light, that is of prime importance for optical
triangulation, may be classified in three various types of
reflection. Each of those three types of reflection is
characterized by the geometric appearance of the light
diffusion. These are the specular reflection share, the
Lambert reflection distribution share and the share
represented by Gaussian reflection diffusion.
Specular reflection is a reflection without diffusion
and ideally follows the reflection law. Since the incident
light is perpendicular to the diffusive surface, this
component of the reflected light is not significant for
laser proximity sensor. Moreover, under specific
conditions, specular component can interfere with
usable reflected components and generates reading
uncertainties. For those reasons, the measuring systems
VOL. 35, No 2, 2007 ▪ 79
that are based on specular reflection differ in design
concept [7].
The Lambert diffuse reflection refers to the case of
uniform reflection that means that the luminance L of
the reflected light is constant for different angles θ,
where θ is measured from the surface's normal axis. In
addition, the light intensity I of the reflected light
follows the relation:
Iθ = I 0 cos θ ,
(9)
independently of the angle of incidence. White paper,
projection screens and random rough surfaces have a
very large share of Lambert reflection. A Lambert
reflector is thus characterized by the fact that the
reflected light is visible under the space angle of π
steradians. In reality this angle is smaller and, as it is
reported in [5] and [6], it is strongly proportional to the
power spectral density of the target surface asperities
height function. In general, the Lambert reflection
diffusion share is far favorable for optical triangulation.
Gaussian reflection diffusion means that the
reflected light basically follows the law of reflection,
but the reflected light is more or less scattered around
the reflection angle (side leakage). The light intensity of
Gaussian diffuse reflection has a Gaussian scattering
profile whose terminal points define the double beam
angle φ. Scattering angle is very seldom greater than
25°. Gaussian reflection share in some cases helps
optical triangulation, but in general, it can cause some
uncertainties, especially in case when PSD detector is
used and diffuse target surface is inclined.
generally termed as roughness, while the structure at the
macro level is termed texture and waviness. The texture
in this particular case is generated by underlying textile
cords. Waviness is irregular macro feature of
manufactured RCS caused by internal stresses which
are, in general, the consequence of non uniformity of
cord tension.
Gradual motion of the RCS surface in lateral
direction, which typically occurs during the scanning
motion, produces very dynamical changes in imaged
spot profile. In Fig. 4 are shown successive light
profiles captured by the same optical sensor as this one
shown in Fig 3, when target RCS sample is moved
incrementally in lateral direction with steps of 100µm.
The imaged spot profile can be distorted even greater in
case when small shine areas exist in the RCS surface.
These spots are easily generated when processed rubber
compound is locally overheated due to unfavorable
conditions of calendering process. Each shine area
behaves as small mirror which reflects significant part
of the incoming laser beam into single direction. This
reflected light component results in intensive distortion
of imaged spot profile.
Figure 4. Imaged spot profile variation during incremental
lateral motion of target RCS surface (six successive steps
of 100 µm, LP filtered).
Figure 3. Imaged light spot profile captured by 2048 pixel
one-dimensional CCD photodiode array.
Typical profile of imaged spot reflected from RCS
sample surface is shown in Fig. 3. This profile is
generated by one-dimensional photodiode array with
2048 sensing elements, i.e., pixels. It is clear that
captured profile is noisy and significantly differs from
theoretical Gaussian bell shaped profile which can be
normally obtained under ideal measuring conditions and
uniform properties of diffuse reflective target surface.
Such profile mainly resulted from non uniform optical
conditions of the measured sample and changes in
surface reflectivity. CR has a highly structured surface
composed of asperities at micro level and regular
texture at macro level. The structure at the micro level is
80 ▪ VOL. 35, No 2, 2007
Under above described optical conditions accurate
and fast triangulation in RCS measurements is a very
demanding engineering task and special algorithms
should be used in estimation of true distance of
measured sample surface.
2.4 CR surface inclination
In case of inclined diffuse target surface, i.e., when the
angle of light incidence differs from π /2, two types of
reading uncertainties can be generated. The first one is
related to the distortion of reflected light intensity
profile. Only in case when incidence angle is π /2 the
reflected light is entirely free of specular component and
Gaussian component may be neglected. In other cases,
FME Transactions
total reflection is composed of Lambert and Gaussian
component. In RCS measurements the specular
component are frequently present too. The result is a
distorted image profile, which generates in that way
measuring error.
The second type of reading uncertainties is so called
light shadowing error, when diffuse reflected light is
physically restricted, completely or partially, to reach
detector or when the image light intensity is so week to
properly excite the detector. The presence of shadowing
conditions most frequently generates reading dropouts.
RCS has textured surface of a corrugated form, i.e.,
regular waves that follows the cord pattern on a macro
level (typical wavelength ranges from 1 to 3 mm). The
RCS waviness appears for optical triangulation as a
periodical change in inclination of diffuse target surface,
providing nominal measuring conditions only within the
narrow top area of each wave. Therefore, the most
reliable measuring results can be expected in these areas
only.
3. EFFECTIVE THICKNESS
RCS thickness is difficult to define because RCS is
compressible and its surface is highly textured. Filtering
of measured data in a way defined by ISO 13565-1:
1996 and ISO 11562: 1996 is in general not applicable
due to potential presence of fragmented or incomplete
vector of measured data. Also, highly textured surfaces
measured by triangulation sensor has inherent source of
reduced precision on sloped and valley areas as
described before. In order to provide reliable method
capable to be effective under these circumstances in this
paper is proposed effective thickness estimation method
based on statistical characterization of RCS surface.
Surface characterization techniques can be classified
as statistical methods, spectral height correlation or
auto-correlation methods, or fractals and self-similarity
methods [7, 8]. In dimensional metrology surface
characterization is mainly performed using statistical
three-layer surface model and linearized material ratio
curve [9]. Within this approach the rough surface is
decomposed on the layer which contains protruding
peaks, the layer which contains the core material of
roughness profile, and the valleys layer.
Decomposition of rough surface on tree layers, and
statistical characterization of each of them, can be used
in RCS effective thickness estimation. Such
characterization is closely related to the manufacturing
process. Calendering is naturally slow and inertial
process and consequently, statistical properties of the
generated CR surface will change slowly in time.
Therefore thickness estimation based on parameters of
linearized material ratio curve can be performed with
equal accuracy over continuously acquired sensory data,
or the data which are fragmented.
Direct application of surface characterization based
on material ratio curve in RCS thickness estimation is
not possible. It must be extended to textured surfaces
before. Moreover, some additional adaptations are
necessary when thickness estimation is performed by
two-sided measurement, since in this case the measured
profile is obtained by superimposition of two different
FME Transactions
surfaces, i.e., upper and bottom surface of RCS, each of
them scanned by its own laser triangulation sensor (this
will be discussed in more detail in the following text).
3.1
Surface characterization
For thickness measurement task it is important to
determine, in percent, the material portion MR1 that
separates the protruding peaks from textured surface
core profile.
If it is assumed that RCS thickness variation z(x)
corresponds to the stationary Markov process [10], then
the value of thickness for any lateral coordinate x
belongs to the same distribution. In this case we assume
Gaussian distribution N ( µ , σ ) . This assumption is
confirmed by experiments. Figure 5 shows the typical
texture profile of CR sample scanned by laser
proximeter with the sampling rate of 10 kHz and
scanning speed of 50 mm/sec. The measurements are
performed in laboratory conditions. It is clear that
thickness variation z(x) of scanned texture profile is well
correlated with normal distribution within the
probability interval [0.05 0.95], and therefore CR
surface can be considered as Gaussian surface.
Figure 5. Scanned texture of RCS sample measured from
flat reference surface (up) and corresponding normal
probability plot (down).
Introducing so-called indicator function I meaning
that:
1 if z ( x) > δ E
I ( x) = 
0 othervise ,
(15)
VOL. 35, No 2, 2007 ▪ 81
δE
Figure 6. Example of measured RCS texture profile and corresponding material ratio curve with its smallest gradient linear
approximation derived in accordance to proposed algorithm.
where δ E is height from arbitrarily chosen reference
line, material portion Mr1 in the interval x∈[0, L] can be
defined using the following relation:
L
Mr1 = ∫ I ( x)dx .
(16)
0
Expectation for such defined material portion is:
L
 L
E ( Mr1) = E  ∫ I ( x)dx  = ∫ P { z ( x) > δ E } dx (17)


0
 0
and since:
δ
P{z ( x) > δ E } = 0.5 − Φ  E
σ

,

(18)
it follows:

 δ 
E ( Mr1) =  0.5 − Φ  E   L .
 σ 

(19)
Mathematically, material ratio curve is equivalent to the
cumulative distribution F(z) of RCS thickness variation
in a given interval:
( z − µ )2
−
2
df ( z )
1
=
F ( z) =
e 2σ .
dz
σ 2π
(20)
The difference is that the coordinate system is rotated
and mirrored only (see Fig. 5).
The equivalent straight line that linearizes material
ratio curve can be derived using similar approach as in
ISO 13565, but instead of using secant, the proposed
method is based on linear regression of the window that
includes 40% of totally measured data points, or
equivalently ∆Mr = 40%. Although it is computationally
intensive such method of linearization is much more
robust than the method based on secant.
The location of the core profile central axis is
defined by the window which has the linear regression
with the smallest gradient. Since the value of the
gradient determines the width of the core profile,
82 ▪ VOL. 35, No 2, 2007
selection of the smallest gradient is at the same time
selection of the narrower core profile. The smallest
gradient search algorithm can be easily performed by
sliding the regression window iteratively, starting from
Mr = 0% and moving to the right. Contrary to the secant
method the search algorithm for core profile central axis
based on minimum gradient linear regression is very
stable and insensitive to local irregularities that
normally can occur in material ratio curve. This is very
important for real time application.
Above described procedure of statistical surface
characterization based on material ratio curve and threelayer texture representation is shown in Fig.6. The data
used in Fig. 6 are the same as those used in Fig 5. Since
they are well correlated to normal distribution, the shape
of obtained material ratio curve is very similar to S
shape of the normal cumulative distribution function.
The upper limit which separates the protruding peaks
from texture core profile is determined by thickness
value of linear regression line for Mr = 0%, while the
lower limit which separates the deep valleys is
determined by thickness value for Mr = 100%.
In case of ideal Gaussian variation of RCS surface
texture, the central region is located at the interval Mr =
[30%, 70%] and the smallest slope of corresponding
linear approximation can be derived directly from (20):
k = −σ 2π ,
(21)
which further leads to the analytical formulation of
material ratio curve linear approximation:
δ = −σ 2π ( Mr − 0.5) + µ .
(22)
If core profile of RCS surface texture is determined
by Mr = 0%, and Mr = 100%, and consequently core
boundaries can be defined directly from (22):
1
2
1
2
δ CORE = [ µ + σ 2π , µ − σ 2π ] .
(23)
It is important that ideal Gaussian surface statistical
characterization is completely defined through two
parameters, i.e., mean value and variance of measured
data. This is true regardless of their completeness. Only
FME Transactions
what is necessary to be satisfied is the size of collected
data which must be sufficient enough to estimate normal
distribution parameters for adopted degree of certainty.
The material ratio curve and core prifile boundaries for
ideal Gaussian suface are shown in Figure 7.
3.2 Statistical definition of effective thiskness
Normally, effective thickness is the distance between
reference surface that supports RCS sample and upper
limit of RCS surface core profile, or equivalently, the
intersection point of linearized material ratio curve (22)
with abscise Mr = 0%. In case that RCS surface is ideal
Gaussian surface, effective thickness can be analytically
expressed by the following equation:
1
δ EFF = µ + σ 2π .
(24)
2
Introducing (24) into (19) corresponding material
portion Mr1 can be calculated:
1

(25)
Mr1EFF = 0.5 − Φ 
2π  = 0.105 .
2

It means that 10.5% of material ratio belongs to
protruding peaks. By selecting other values of abscise,
i.e., Mr greater than 0%, one can calculate lower
effective thickness and greater rejected material portion.
Physically, this is related to compressibility of the RCS.
Any mechanical gauge applies some pressure and
therefore affects the thickness. Percentage of rejected
material portion which is leaved to protruding peaks
layer may be interpreted as rising up of contact force in
contact measurement methods (thickness measurement
by micrometer caliper gauge for instance, which is
standard measuring instrument in manual thickness
measurement, applies precisely defined pressure to the
contact foot with standardized diameter).
can be defined as a distance between upper limits of the
texture core profiles of two RCS surfaces. It means that
two material ratio curves F1(z) and F2(z) were
estimated from sensory data and their linear
approximations are derived using relation (22).
Proposed surface characterization method for RCS
effective thickness estimation may be interpreted as a
method for robust recovering of lost information
content, caused by shadowing effect in differential laser
triangulation scanning of RCS surface. Therefore, it is a
good solution for solving the problem of extensive
dropout rate which fequently appears in RCS thickness
measurement based on commercially available single
triangulation laser proximity sensors. Moreover, in
proposed surface characterization method, data which
belong to valleys are not necessary in effective
thickness estimation. This is of high importance,
because even if laser triangulation sensor is able to
acquire valid measurements, such measurements are
critical in respect to achieved accuracy (influence of
distorted image profile as discussed before).
4. CONCLUSION
The outline of advanced technology for in-process RCS
thickness measurement by laser triangulation is
presented. Analytical model of laser triangulation and
the most critical problems in distance measurements of
the objects having highly textured surfaces are
considered in details. Based on this analysis the new
method for noncontact thickness estimation of RCS is
proposed. This method is based on three-layer
structured
surface
textured
and
statistical
characterization of these layers. It is proved analytically
and by experiments that the RCS texture is Gaussian
type of texture, which further enables accurate and
robust thickness estimation only using identified
parameters normal distribution of scanned RCS surface
texture. Results obtained from laboratory experiments
show that the new method is capable to replace the
existing methods based on radiation sensors, with better
measuring properties and no environmental risk.
REFERENCES
Fig.7: Standardized material ratio curve for ideal Gaussian
texture (µ = 0 mm, which gives k = -2.5066σ, δcore1 = 1.2533σ,
δcore2 = -1.2533σ).
By varying value of material ratio Mr1 specific kind
of filtering is performed. This filtering removes
outlaying data points, peaks and debris, leaving only
core material that is of primary interest in thickness
measurement. Also, it rises up the accuracy and
robustness of entire measurement process.
In case that material ratio curves are defined for
both, upper and lower surface, the equivalent thickness
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84 ▪ VOL. 35, No 2, 2007
МЕРЕЊЕ ДЕБЉИНЕ ГУМИРАНОГ КОРДА
ПРИМЕНОМ ЛАСЕРСКЕ ТРИАНГУЛАЦИЈЕ
– Део I: Технологија
Петар Б. Петровић
У раду је презентиран концептуални оквир
технологије мерења еквивалнентне дебљине
гумираног корда применом оптичке триангулације.
Детаљно је изложен аналитички модел ласерског
проксиметра и разматрани су основни проблеми
везани за функционисање и примену ласерске
триангулације у мерењу дистанце објеката са
изразито текстуираном површином која поседује
неуниформна оптичка својства. Предложена је нова
метода која омогућава робусну и високопрецизну
естимацију ефективне дебљине гумираног корда.
Ова метода је базирана на структуирању површи на
три слоја и статистичкој каракетеризацији ових
слојева. Показано је да текстура гумираног корда
одговара класи Гаусових површи, на основу чега је
могуће прецизно и врло робусно израчунавање
еквивалнетне дебљине само на основу естимираних
параметара нормалне расподеле скенираног узорка
површи.
Лабораторијски
експерименти
су
потврдили практичну употребљивост ове методе и
створиле реалне основе за развој нове технологије
мерних система који ће моћи да замене
конвенционална решења базирна на сензорима са
природним или вештачким изворима радиоактивног
зрачења.
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